It can be used to enumerate all subsets of size N from a set of size M. Start with 1 << N - 1, and then repeatedly call this function until the value is larger than 1 << M. Every subset of size N will be visited, in order.

Can you explain what you mean by "set" and "subset"? What do they contain? How they're represented? I can't make heads or tails of your answer as-is.

Take a 64 bit number and treat it like a bit field where each bit represents inclusion/exclusion of an element in a set S of size 64. Thus every number with M 1s represents a (distinct) M-sized subset of S

Iterates through all possible N-combinations of a set that has M elements?

Every bit in a bitfield represents a "thing". The bitfield represents a collection of distinct things. If bit "i" is 1, then the corresponding thing "i" is in the collection.

That's certainly a very smart way of doing so.

Years ago, I had a similar need and I consulted TAOCP to find the “standard” algorithm to do so, which is done by a binomial tree. The tree T is defined recursively as T(0) = nil and T(n) = [Cons(0, T(0)), Cons(1, T(1)), ..., Cons(n-1, T(n-1))]. There's no need to construct the tree explicitly; it's just a conceptual formalism that helps formulate an algorithm to traverse the tree.

The text did mention using bitwise operations to do so; in fact it says it presents a “remarkable sequence of seven bitwise operations that will convert any binary number to the lexicographically next t-combination” but I haven't been able to find those seven operations.

This can be used generate all bit sequences over a particular range that have the same Hamming weight. I have needed that before when testing error-correction code decoders to make sure they properly correct all of the possible error patterns that they should be able to.

It's filtering by popcount effectively [0] and crops up quite a bit.

[0] https://vaibhavsagar.com/blog/2019/09/08/popcount/

I misunderstood the task

Chess engine stuff, at the very least. With an integer mask representing an 8x8 board and 1s representing a single type of piece, you can find all subsets of pawn positions etc.

I've used this to enumerate grids with a certain number of open and closed cells (0 and 1 bits). It is simply the next permutation of a bit string. C++ offers this in its standard lib, but that version is slower by factor 1000 or so.

I've also tested this with arbitrary bit-width numbers (LLVM can do that) and it worked fine. I've not checked if the code is the exact same tho.

>slower by factor of 1000

It's also for generic iterables.

I'm going out on a limb and say "bloom filters" so it has applications in fast filtering, seen-count, DB stuff like parallelism, discrete-different buckets, partially ordered sets being applied in a stream of events...